I seem to remember reading somewhere that the clearance problem was in the curved tunnels before Midland line trains reached the Widened Lines. The belief that coaching stock on the Widened Lines themselves could be no longer than 57 ft was eventually proved to be a myth, I believe.
The biggest problem with using the Met and the Widened Lines (even more so before WW1) must have been the intensive services already using these lines. Also, there was the steep gradient up from Snow Hill to Ludgate Hill.
Going back to my suggestion about using the West London line, the area north of Willesden Junction appears to have been relatively undeveloped at the start of the 20th Century, so building a connection from the Great Central would not have been particularly difficult - barring objections from the LNWR, anyway. I am not sure what the best route south of the Thames would have been though.